Scaling law for the contact-propagation regime of first-passage percolation

We study first-passage percolation on a lattice with a fraction p{}pc of bonds assigned zero time delay, the others having finite delays governed by the cumulative distribution F(x). This ``contact-propagation'' regime exhibits criticality analogous to the random superconducting network. We derive, and confirm numerically, a scaling law that relates the divergence of the first-passage velocity near the percolation threshold pc to static percolation exponents and to F(x).